Some new inclusion sets for eigenvalues of tensors with application

Abstract

In this paper, we are concerned with the eigenvalue inclusion sets for tensors. Some new \emph{S}-type eigenvalue localization sets for tensors are employed by dividing $N=\{1,2,\ldots,n\}$ into disjoint subsets $S$ and its complement. Our new sets, are proved to be tighter than that newly derived by Huang et al. (J. Inequal. Appl. 2016: 254, 2016).  As applications, we can apply the proposed sets for determining the positive (semi-)definiteness of even-order symmetric tensors. Some examples are given to show the sharpness of our new sets in contrast with the known ones, and verify the effectiveness of those in identifying the positive (semi-)definiteness of tensors.